The adsorption of gases onto porous solids is a primary method by which the morphology of solids is characterized. Specifically, the surface area, pore volume and pore size distribution can be inferred and calculated from analyses of the relationship between the volume adsorbed and the pressure of a physically adsorbing gas. These morphological characteristics (surface area, pore volume and pore size distribution) are employed in the design and analyses of solids employed in catalysis, as adsorbents or for separations.
A variety of theories are employed to interpret the adsorption or desorption isotherms in order to infer the total surface area of the solid and the dimensions of any void space within or between individual particles. The specific theory and equations employed in the analyses depends on the range of dimensions of pores being analyzed, on the specific adsorbent/adsorbate being analyzed, and on the preference of the person performing the analyses. Nitrogen sorption at 77 K. or Argon sorption at 87 K. (or 77 K.) are often employed in the analyses, although the improved techniques and system are not limited to the use of these adsorbates at these temperatures.
Crucial to each theory and its application to the analyses of the data to infer the morphology of porous solids is the assumption that the data being analyzed represent equilibrium sorption isotherms. The present invention provides a novel apparatus and method to obtain equilibrium adsorption isotherms. Specifically, the system measures multiple data points of the equilibrium sorption isotherms at low pressures (e.g., significantly less than a relative pressure of 0.1, i.e., 0.1 atmospheres for measurement of adsorption at the boiling point of the sorbate) in a reduced period of time.
Several systems and approaches have been patented and are available to measure sorption isotherms. Most of these have involved measurement of sorption for pressures within two orders of magnitude of the saturation pressure (i.e., at relative pressures from 0.01 to 1.0). U.S. Pat. No. 3,850,040 discloses an apparatus and a method by which the amount of gas admitted to the sample system is determined by calculation and manipulation of the pressure of the sorbing gas added to or removed from above a sample maintained at the temperature at which the sorption is to be measured. Examples demonstrate how the amount adsorbed over equal increments of relative pressure (e.g., changes in relative pressure of 0.04) from 0.04 to 0.2 may be measured initially to calculate the surface area of the sample by the BET theory. Subsequently, pore volume analysis is accomplished by "extending the previously-described dosing sequence" along a predetermined series of partial pressures which culminate at a desired pressure, such as 0.99 Po. A diffusion pump (backed up by a roughing pump) is employed to evacuate the sample and a single diaphragm pressure transducer is employed to measure the pressure at which sorption equilibrium is achieved. A method is also described by which desorption is measured from a relative pressure of approximately 0.99 in similarly predetermined increments.
Comments on U.S. Pat. No. 3,850,040
The method and equipment described in this patent are incapable of measuring pressures over more than two decades of relative pressure. The pumping system is inadequate for high resolution adsorption isotherms since minimum tubing and valve sizes are not specified, and a single stage diffusion pump cannot achieve low enough initial pressures. Further, multiple transducers are required to measure pressures accurately over the broad spectrum of pressures (greater than a factor of 10000) required for high resolution adsorption isotherms. Further, there is no provision to vary the increments of adsorbate volume introduced by the amount required for high resolution adsorption (greater than a factor of 100) and there is no provision for changing and monitoring the achievement of equilibrium in volume adsorbed between doses. This is crucial to assuring equilibrium measurements in a reasonable time, particularly commencing at pressures substantially below 0.001 atmospheres (P/P.sub.o &lt;&lt;0.001 for a gas at its boiling point) and covering greater than three orders of magnitude in pressure. The current invention discloses all of these novel approaches in equipment and methods of measuring isotherms.
U.S. Pat. No. 4,566,326 discloses an automated apparatus by which the sorption isotherms can be measured independently for a plurality of samples. Several pressure transducers (one per sample) are employed to independently monitor the pressure over several samples essentially simultaneously. A method is described by which gas is admitted from a manifold (at a separately controlled and measured pressure) to each of several samples. This patent describes a system which makes the measurement of sorption isotherms more efficient by conducting the measurements in parallel. The described measurements commence with the calculation of the surface area by adsorption measurements over relative pressures (e.g., from approximately 0.05 to 0.2) through the adsorption and desorption within the pores (nearly up to a relative pressure of 1.0).
Comments on U.S. Pat. No. 4,566,326
This Patent discloses the use of multiple pressure transducers. However, the transducers all span the same range and are each connected to different samples. This invention discloses a single apparatus and methods by which it can be operated to measure adsorption isotherms for several samples in parallel up to less than a factor of 100 in relative pressure. There is no provision to measure a broader range of pressures. There are no disclosures which allow for the equilibrium measurements to start at low relative pressures (P/P.sub.o &lt;0.01) and to span more than two orders of magnitude in relative pressure.
U.S. Pat. No. 4,762,010 discloses an apparatus by which gas is leaked from a bulb of known volume over the sample at a rate that is claimed to be sufficiently low to maintain equilibrium. The patent asserts that in this manner points in the adsorption isotherm can be determined continually, and that leaking gas from a controlled volume system at reduced pressures over the sample can provide better control of the amount of gas exposed to the sample. These improvements are claimed to enable the measurement of adsorption isotherms for samples with extremely large surface areas and pore dimensions down to five angstroms. The patent is based on the fact that, "Most prior work in this field has involved larger dimensions." As discussed in detail in this 1988 patent, the systems, "presently available do not satisfy the needs of the art."
This patent is based upon an improvement over U.S. Pat. No. 4,487,213 which first disclosed a leak of gas over a sample which is controlled by a mass flow controller (from a source of adsorbent gas above its saturation pressure). The patented improvement utilizes a source of gas that is filled to below the saturation pressure. In this manner the differential in pressure between the source and the sample is decreased. This is most significant for the measurement of adsorption at low equilibrium pressures (below 0.1 atmospheres) where the smaller pores are filled. By controlled increases in the pressure of the source (employing a series of reservoirs up to 5 liters in volume), a large range of pressures can be studied with reduced differences in pressure between the source of the adsorbing gas and the sample compared to a controlled flow from a source at a single pressure. In all embodiments of this invention, the adsorbing gas is admitted to the sample by flow through a flow restrictor which is claimed to keep the rate of gas admission low enough to maintain adsorption equilibrium. The volume admitted to the sample is calculated from measurement of changes in the pressure at the fixed volume source during the controlled leaking over the sample and not by measuring and controlling the flow. The patented apparatus employs two devices for pressure measurement over a range of pressures. A diffusion pump "possibly assisted by a forepump" is employed during desorption studies to as low as 10.sup.-5 Torr.
Two additional types of experiments are described in U.S. Pat. No. 4,762,010 wherein constant pressure adsorption measurements can be made by controlling the leak valve and monitoring the pressure of adsorbate over the sample, and wherein "pulses" of gas are admitted or removed by unrestricted flow between the sample and the reservoir for a prescribed period of time. Both of these methods collect non-equilibrium data, presumably to measure transient transport/diffusion, and are not relevant to the methods and apparatus of the current invention which describes improvements to measure sorption at equilibrium.
Comments on U.S. Pat. No. 4,762,010 and U.S. Pat. No. 4,487,213
U.S. Pat. No. 4,762,010 is the first to have claimed the capability to measure equilibrium adsorption isotherms over several orders (greater than a factor of 100) of magnitude of pressure. This is accomplished by employing several reservoirs of the adsorbing gas at variable pressures. However, U.S. Pat. No. 4,762,010 claims that equilibrium adsorption isotherms can be measured during the leaking of gas from the reduced pressure into the adsorption system. They point out that the flow control disclosed in U.S. Pat. No. 4,487,213 is inadequate for pressures in the 0-15 Torr range. All of the independent claims in U.S. Pat. No. 4,762,010 (claims 1, 11, 15, 16, 17, 27) employ a "flow restrictor". We find that any continuous introduction of an adsorbing gas will not be at equilibrium at the lowest pressures (P/P.sub.o &lt;0.001). The apparatuses disclosed make no provisions or claims to achieve the lowest pressures (below 10.sup.-5 Torr) that we find are necessary during pretreatment, i.e., before the initial pressure measurements. We find that two pressure measurement devices with two full scale ranges are inadequate to accurately measure pressures from 1000 Torr to less than 10.sup.-5 Torr. The 1 Torr pressure transducer disclosed employed in U.S. Pat. No. 4,762,010 is not accurate below 0.01% of its range, i.e., below 10.sup.-4 Torr. The apparatus disclosed in U.S. Pat. No. 4,762,010 FIG. 3 is far more complex than is necessary if gas is not flowed over the sample.
U.S. Pat. No. 4,972,730 discloses an apparatus that automatically measures the saturation pressure after measurement of the adsorption isotherm. The purpose is to precisely calculate the relative pressure for subsequent calculations of morphological characteristics such as surface area and pore dimensions. This patented series of measurements and the associated apparatus are based on a claimed improvement in the determination of saturation pressure by direct measurement employing the same pressure measurement devices as those employed during the determination of the adsorption isotherm. There are no disclosures in U.S. Pat. No. 4,972,730 to enable adsorption measurements at relatively low pressures.
Improvements and Embodiments of the Current Invention
The apparatus and method of this invention represents a substantial improvement over known systems to measure equilibrium adsorption isotherms (volume adsorbed versus pressure at essentially constant temperature) accurately for pressures commencing significantly below 0.01 atmosphere and spanning several orders of magnitude in pressure (e.g., 0.01&lt;P/Po&lt;0.00001, where Po is the saturation pressure of the adsorbent). The system employs larger tubing (&gt;0.25 inch in outer diameter) and valves for the majority of the volume of the flow path from the sample to source of the vacuum than in conventional systems. The system uses higher capacity (lower ultimate vacuum) pumps to evacuate the sample than are found in systems currently patented for the analyses of adsorption isotherms. The invention doses increasing (and/or possibly decreasing) incremental amounts of a sorbing gas over the sample being characterized. The invention allows a variation in the amount of sorbing gas exposed to the sample during the measurement and a variation in the time between the successive additions (or removals) of sorbing gas exposed to the sample. The invention employs at least two pressure measurement devices, one of which may involve changes in its maximum range of pressure within the same unit.
These measurements are employed in the characterization of the void dimensions of microporous (dimensions less than 20 .ANG. in diameter for an equivalent cylindrical pore) solids. These improvements enable the measurement of equilibrium adsorption isotherms over several orders of magnitude in pressure to be completed in a minimal period of time.
Measurement of Sorption Isotherms at Low Pressures
In general, the major difficulties in the measurement of adsorption isotherms at low pressures (in the order of 10.sup.-5 Torr in the case of micropores) is the addition of small amounts of adsorbate gas and the accurate measurement of the resulting equilibrium pressures. In order to overcome these difficulties we developed a modified static technique and apparatus to employ this technique.
The difference between our technique and the techniques employed by prior investigators is that the adsorbate gas is dosed over the sample through a dosing valve (or combination of vacuum valves). In this way, the amount of adsorbate gas admitted into the system is measured and is controlled. Each dose corresponds to increases in relative pressures (P/P.sub.o) of less than 10.sup.-6 per dose for Ar at 87 K. or N.sub.2 at 77 K. for the initial doses of gas over the sample. The system is allowed to equilibrate for a variable time before the next aliquot of adsorbate is introduced over the sample.
Helium may be first added into the system to determine the "dead volume" of the sample and sample cell from the relationship between pressure and volume added. The dead volume is the volume of the sample holder excluding that of the sample itself. After the evacuation of the helium, the adsorbate gas addition follows. Note that helium may be run into the system continuously through a flow controller for the determination of the dead volume in order to reduce the measurement time. An added advantage of the exposure to helium prior to the adsorption measurement is that the large heat transfer coefficient of helium assures rapid equilibration between the sample and the liquid nitrogen or argon temperature baths.
When the adsorbate gas is dosed into the sample cell, the pressure goes up. As adsorption takes place, the pressure decreases. The system is allowed to equilibrate before the next aliquot of adsorbate is dosed. Equilibrium is reached when the pressure no longer changes with time. The time required for equilibrium to be achieved varies from more than 30 minutes for the initial doses at residual pressures below 10.sup.-4 torr to less than 3 minutes for pressures approaching one torr (P/Po.about.10.sup.-3). There is no known method by which a system that employs continuous flow of gas over the sample can measure equilibrium pressures during the flow process for the measurement of adsorption at the low pressures required for the adsorption and filling of pores less than 2 nm in dimension.
The size of the dose is varied throughout the measurement of the isotherm. Initially doses in increments less than 10.sup.-3 torr (P/Po&lt;10.sup.-6) are added. If equal size doses were added, over a thousand doses would be required to span the pressures to P/P.sub.o =10.sup.-3 in increments of P/P.sub.o &lt;10.sup.-6, as required for the initial doses. If equal times were allowed for equilibrium between doses of adsorbent, one thousand increments of equilibrium time would be needed. The amount of the gas dosed is varied by up to an order of magnitude (increasing with pressure) and the time for equilibrium (decreasing with pressure) is also varied varied by up to an order of magnitude to assure accuracy in the equilibrium pressure and to minimize the total time of the measurement.
Conventional automated systems employ 10-Torr and 1000-Torr (maximum range) pressure transducers for the measurement of pressures at equilibrium. The transducer manufacturers claim accuracy down to &lt;0.1% of their full range. So, the combination of these transducers will accurately measure pressures from 0.01 up to 1000 Torr. For adsorption of a gas at its saturation pressure this means accurate measurement in relative pressure, P/Po, from 10.sup.-5 to 1. So, in order to study any adsorption that may occur over ranges in relative pressures from 10.sup.-6 to 10.sup.-3, where micropores (&lt;2 nm in diameter) fill, it is necessary to employ a more accurate capacitance manometer. We have used a 1-Torr, high accuracy capacitance transducer to obtain measurements of the pressure at equilibrium in the range of 10.sup.-6 &lt;P/P.sub.o &lt;10.sup.-2 in our apparatus. The range of this transducer is marginal for this application and is not adequate to monitor the initial evacuation of the sample (to below 10.sup.-5 Torr). A Tylan MVG transducer may also be employed to accurately measure the pressure. This unique transducer uses dual diaphragms to measure the pressure accurately over variable ranges. Specifically, this transducer measures pressures over a range of 1 torr down to a range of 100 microns in pressure. The measurement range is selected by an electronic circuit and may be changed by the operator or by a computer program which indirectly controls the transducer. A 1000-Torr transducer was used for the measurement of pressures higher than 1 Torr.
The calculation of the volume adsorbed at a given relative pressure in a fixed volume system involves calculating the amount of adsorbent still in the gas phase. This is subtracted from the total amount added to the system at this point. The difference is the amount adsorbed. The amount of adsorbate in the gas phase, a "dead volume correction", is calculated from the product of the dead volume of the adsorption manifold (including that over the sample and accounting for the possible differences in temperature) multiplied by the measured pressure. Inaccurate calculations of the amount adsorbed are a result of inaccuracies in the dead volume, in the pressure measurements, or in the corrections for differences in temperatures of the volumes which comprise the dead volume. Prior adsorption systems developed primarily for measurements at relative pressures above 0.01 decrease the inaccuracies by minimizing the dead volume. This is accomplished by employing small volume valves and small diameter tubing to interconnect the parts of the manifold.
Adsorption in micropores occurs at substantially lower pressures than for samples which contain larger pores. Pores less than 2 nm in dimension (diameter or width) are filled at relative pressures less than 0.001. Under these conditions the dead volume correction is small because the relative pressure is small. It is less important to minimize the dead volume in order to achieve accuracy for measurements of adsorption which occurs at low relative pressures (i.e., less than 0.01).
For accurate measurements at low relative pressures, it is necessary to evacuate the sample and manifold to even lower pressures than the pressure of the initial measurement. Smaller tubing and valves in the system make the evacuation more difficult to achieve and require longer times to achieve these low pressures. Further, smaller tubing and valves mean that there is an increased possibility that there are differences in the pressure at different volumes of the system being evacuated; thus, pressure measurements are less accurate.
The present system avoids the dominance of small diameter tubing and small valves between the vacuum pump and the sample employed in prior adsorption systems. The majority of the tubing and valves which connect the vacuum system and the sample are larger than 0.25 inch in inner diameter, ID. Preferably this tubing is 0.5 inch ID or larger. The only tubing that most directly connects the sample and the high vacuum pump that is less than 0.5 inches OD is that volume which connects the sample to the adsorption manifold. This is because the tubing which connects immediately to the sample is less than 0.5 inch ID in order to reduce any inaccuracies which would occur if there were any variation in the height of a thermal bath in which the sample is immersed.
To achieve the low initial pressures required for the measurement of adsorption in small pores, it is necessary to employ an efficient pumping system capable of achieving a high vacuum (low pressure) over the sample. This should be at least an order of magnitude (and preferably at least two orders of magnitude) lower in pressure than the initial pressure at which adsorption may occur. Adsorption occurs below a relative pressure of 10.sup.-7 to 10.sup.-6 for adsorption in pores of a diameter less than 0.4 nm. Preferably, the pumping system should be able to efficiently evacuate the manifold and sample to less than a relative pressure of 10.sup.-9. The vacuum systems employed for most of the current automated adsorption systems employ oil diffusion pumps with a rough, backing pump. This is not adequate to reach these required vacuums efficiently. A turbomolecular pump is employed in the system being patented. Other vacuum systems could also fulfill these requirements.
Summary of Principles For the Efficient, Accurate Measurement of Adsorption At Low Relative Pressures On Which This Invention Is Based
a) The pressure of adsorption is measured by more than one pressure transducer and/or employing transducers that have more than a single maximum range. The range of the pressure measuring device is such that pressures of 0.001 torr (and preferably 0.0001 torr, i.e., ca. 10.sup.-7 atm.) are measured accurately.
b) Gas is dosed over the sample and the volume of the gas dosed between measurements is changed as the measurement pressure changes.
c) The time between doses varies as the time required to achieve equilibrium.
d) The tubing connecting the pumping system and the sample and the sample and the pressure transducers is of diameter greater than 0.25 inch in inner diameter ID (and preferably equal to or greater than 0.5 inches OD), however, the tubing immediately connected to the sample may be of OD equal to or less than 0.25 inch. The volume of this smaller diameter tubing should be less than 10% of the total volume of the closed system into which the adsorbing gas is dosed.
e) The pumping system employed to evacuate the closed system into which the adsorbing gas is dosed should be capable of reaching pressures less than 10.sup.-8 atmospheres in this system (and preferably less than 10.sup.-9 atmospheres pressure).